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Topic

Integration

Asked 5 times in ESE over 2 years (2022–2024), peaking in 2022.
5
PYQs
1
Exams
2
Years active
2022–2024
Span
2022
Peak
5/5
Answers
📅 Full chronological timeline →

Key insights

  • Most tested in ESE — 5 of 5 PYQs
  • Most asked in 2022
  • Recurs across 2 years (2022–2024)

Across exams

ESE · 5

How the concept evolved

422
124
Rising — more than half its appearances (5 of 5) are since 2016.

Related concepts

Ideas UPSC tests alongside this one — keep exploring.

Sample questions

You've seen the pattern — here are a few of the actual PYQs.
ESE2024
Suppose we do not know the path of a hang glider, but only its acceleration vector a(t) = −(3 cos t)i − (3 sin t)j + 2k. We also know that initially (at time t = 0) the glider departed from the point (4, 0, 0) with velocity v(0) = 3j. What is the glider's position as a function of t?
  1. A r(t) = (1 + 3 cos t)i + 3 sin tj + t²k
  2. B r(t) = (−1+3 cos t)i + 3 sin tj + t²k
  3. C r(t) = (1 − 3 cos t)i + 3 sin tj + t²k
  4. D r(t) = (1 + 3 cos t)i + 3 sin tj + t²k ✓
✓ Correct answer: (D)
Engineering › Engineering Mathematics & General
ESE2022
The value of ..J( ) dx is 2 2x + 1 0 (take positive values of square roots only)
  1. A 1
  2. B 2
  3. C 3 ✓
  4. D 4 2022 ESE
✓ Correct answer: (C)
Engineering › Engineering Mathematics & General
ESE2022
By integration the area bounded by the three straight lines y 4 - x, y 3x and 3y=x is
  1. A 2 square units
  2. B 3 square units
  3. C 4 square units ✓
  4. D 5 square units
✓ Correct answer: (C)
Engineering › Engineering Mathematics & General

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